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Music is comprised of sound waves. Waves can be modeled mathematically using a Fourier series. So, could we then write music in terms of mathematics by using a Fourier series to represent the sound waves? Would it be worthwhile to do so? Would it have any benefit over traditional music notation?

Music is composed of sound waves, but that's only part of the story. A Fourier analysis would run the risk of including too much information, overlooking the fact that there can be very different interpretations of the same piece.

It might be possible to fudge that point. (After all, compression schemes rely on Fourier analysis, but don't include every detail.) The real point is that to be useful, musical notation has to be something that musicians can efficiently read. To make the case that Fourier analysis would be useful for that purpose would be a pretty heavy lift, I suspect. Compare: it would be possible to give a Fourier analysis of a speech in a play, at least as performed by some actor. But I'd be willing to bet that any actor would find it a lot easier just to have the words written down. Musical notation, like written words and dance notation, is able to do its job precisely because it vastly, massively underspecifies the full detail of what any performance will actually be like. The point here isn't just about leaving room for interpretation. It's about what we can reasonably expect a human brain to process.

 Are there any rationally compelling reasons to believe in a god or gods, which created the cosmos and the things in it?

Nope. But what of it?

"Rationally compelling" is too high bar. If a position really were rationally compelling, a rational person who understood it would have to be convinced. But there's very little in philosophy that meets this standard. There are rationally acceptable ways to believe in God, rationally acceptable ways to believe that there's no God, and rationally acceptable ways to be agnostic.

As for what the reasons are, that's a long story, though I'd caution against thinking they can be reduced to slogans. Of course, the same point goes for more or less all claims that philosophers debate. But somehow, some people seem to think the case of religion is different.

A friend of mine committed suicide recently, and I find myself instinctively trying not only to understand why she did it and the cause and effect of how it happened, but trying to impose meaning -- trying to work out what the "significance" of her death is, and looking to sum up her whole life the way a funeral celebrant might, and say these are the patterns and themes and shape of it, this what it amounted to, this is what it represented, these are the takeaway ethical messages for your own life. But is there really any significance in suicide, is there any point to asking what it means, or is it senseless, like washing the dishes or mowing the lawn or any other physical event or act? And is it disrespectful to try to interpret meaning into someone's life or death or reduce their life to a moral lesson? The process not only feels a little bit like a lie, but also like it objectifies them and takes away from their humanity.

You are obviously grappling with your friend's death, and I appreciate the sophistication and sensitivity evident in your question.

I think it's crucial here to distinguish the meaning or "significance" of suicide from the meaning or significance of your friend's suicide. It's important that we resist what I think of as the easy mystification of suicide. There is an unfortunate tendency to infer from our inability to understand a particular suicide or to imagine ourselves engaging in the act ourselves that suicide is unfathomable, incomprehensible, or beyond reason. The truth is we understand a fair bit about the causes of suicide, have growing knowledge of how to prevent it, and so on. We should not let our emotional reaction to suicide -- whether it be shock, dismay, anger, whatever -- lead us to treat suicide as a "senseless" or trivial act.

That said, what we know about suicide in general can be difficult to extrapolate to particular people and cases. Individual people are in certain ways more complex than our theories about human nature can sometimes capture. I don't think that it's necessarily wrong for you to interrogate why she engaged in this act and to evaluate it morally. But as you say there is the risk that in so doing, you "objectify" your friend or reduce her to her suicidal choices or acts. And that, I agree, you ought not do. She, like anyone, had a history: as someone's daughter, your friend, and so on. Trying to see her suicide as a part of her life, and trying to draw lessons (moral or otherwise) from it, need not require you to reduce her to 'a suicidal person.' Quite the contrary: her suicide can probably only be grasped against the totality of her life. In this respect, your duty to her is the same duty I suspect we have to everyone as we attempt to understand them — to sympathetically, compassionately, and fairly appraise them as the complex wholes as they are, and not distort those wholes only by reference to a single choice or episode in their lives.

Best wishes to you as you work these matters through.

If we all have personal biases (ie. every individual, being unique, perceives the same event slightly differently), how can we trust anyone to provide the real truth?

An incomplete answer, but relevant, I hope.

Suppose the question is: did Prof. Geisler show up for class on Monday? We ask students enrolled in the class. All the students who were there in the room at class time say yes: Prof. Geisler was there. In fact, she arrived on time, and taught a full class.

Let's grant that every person in the room had a slightly different take on exactly what went on in the room at that time. Let's also grant that some of what some people would say happened will be inaccurate, and may reflect their biases and psychological idiosyncrasies. The question, however, is whether Prof. Geisler showed up. There's no reason to think these differences in perception got in the way of judging that.

In one way this is a trivial example, but it reflects something extremely common. Even with our very real quirks and biases, there's an enormous amount of what we perceive and believe for which those quirks and biases are simply irrelevant. Individually, most of these facts may be inconsequential. But when we add them up, we arrive at a shared account of a great deal about the way things are. We don't all live in our own separate worlds. People who claim otherwise strike me as either not really thinking through what they're saying or else in the grip of a bad theory.

Don't many of us regard that "vision" is something like the headlights of a car, casting a beam of light on objects, originating inside the eye? Which is of course completely wrong and the truth is the opposite. Its fairly present in many cultures and even though it is just a mere figure of speech it feels wrong doesn't it?

Do the perceptual systems work from the environment in, or from the perceiver out? In English there are famously two very different groups of perceptual words, one active and one passive: look/see, listen/hear, touch/#feel, smell/smell (i.e. "smell" has two meanings, one for the activity of sniffing out - ('The dog was smelling my shoes'), and the other for a more passive kind of reception of some smell.) In his celebrated 1966 The Senses Considered as Perceptual Systems J.J. Gibson argued that the active seeking out of "information" is more fundamental than passive sensing, and his famous cookie-cutter experiment showed this. If you actively move your hands relative to the object of perception, the percentage of correct identifications is very high. If the stimuli are given to you passively, the percentage drops to under half of what it was. The senses have to be active, and without activity even the passive sensation degrades. This was also shown by some early phenomenological experiments by Katz on grades of paper. It is even true in unobvious ways of vision, as can be seen by the disappearance of objects in the field of vision whose image is stabilised on the retina.

Is it fair for the government to impose something onto people that they did not want or ask for, while still expecting them to carry the burden of it? For example in 2015 the government mandated that all TV stations stop broadcasting in analog and broadcast exclusively in digital. The result of this was billions of dollars wasted in PSAs and handing out converter boxes, millions of portable TV sets ending up in landfills, and many low income families left without TV. The cost of all of this was ultimately left to taxpayers, while the government made 19 billion in spectrum auctions. In other words, the government gained a massive benefit at the expense of the citizens. Can one justify breaking a law that causes more harm than good? Lets say that I am operating a TV station in a rural area with a lot of mountains and bad weather, in which a digital signal would have poor reception. Would I be justified in broadcasting an analog TV signal in this area, even though I am legally prohibited from doing so? As consumers in a free market society, do we not have the right to make these decisions as the circumstances would necessitate. After all, we (more often than not) know the conditions we are dealing with more than the government.

Lots of questions there. I'll offer three comments.

The first is that if citizens simply get to pick and choose the laws they follow, then we don't have laws at all. The question of what makes government coercion legitimate is a big one, and I'm not a political philosopher. But if governments are ever legitimate, then it will also be legitimate to prevent people, by force if necessary, from simply ignoring laws they don't like.

The second comment is about this:

          In other words, the government gained a massive benefit at the expense of the citizens.

I'd suggest there's a confusion here. The government isn't a private corporation. Money that "the government" has is money that the State has, and, if the State isn't corrupt, the government (the institutional embodiment of the State) uses the money for the benefit of its citizens. It's not stowed in secret bank accounts that government officials can draw on for their own benefit.

Finally, is it ever justified to break a law that does more harm than good? It may be, though the State will still have a prima facie justification for prosecuting the lawbreakers. This goes back to the first point: some citizen may believe that some law does more harm than good. But a "state" that leaves these judgments up to individual citizens will not be a state at all. Some people may have enough faith in human nature to believe that anarchy is a better alternative than the State, even if the State is a functioning modern democracy. Most of us aren't convinced, however interesting and difficult problem providing a good theory of the State may be.

Through some years of philosophical study I've become confused about what exactly it means for me to have knowledge. What was once a familiar and seemingly clear concept has now become unfamiliar and obscure. Can it be made clear again for me? Can I ever know whether or not I know? It seems as though the more I read about knowledge the more obscured it becomes.

I don't know the answer to your question, but since this topic interests you, I would recommend you take a look at the skeptical traditions generally categorized as Pyrrhonian and Academic skepticism. One famous device you might use to think about these questions is called Agrippa's trilemma. An ancient chronicler of skepticism called Sextus Empiricus reports that one Agrippa posed the following problem: Justifications for knowledge claims seem problematic because knowledge claims must be justified by other claims, just as premises are needed to justify a conclusion. How are the justifying claims to be themselves justified? Either (1) they are self-evident and self-justifying--but this seems wrong and little better than making assumptions, which justify nothing. Or (2) the supposed justification starts an infinite regress where the supporting claims get justified by other claims and those claims get justified by still other claims, ad infinitum--but an infinite regress doesn't seem like justification. Or (3) the justifying claims run finally in a circle where one set justifies others, which are justified by others, which require the initial claim for justification--but arguing in a circle doesn't justify anything either. Since there's no alternative besides stopping with assumptions, an infinite regress of justifications, or arguing in a circle, and since none of those three offer adequate justification, then it seems that knowledge is impossible. For Sextus's formulation of this trilemma, see his book, _The Outlines of Pyrrhonism_, Book 1, Chapter 15, Line 164 (usually cited as PH 1.15.164). Do you see a way out of Agrippa's trilemma? I confess that as of this moment, I don't.

When you look at non-human animal communication, for instance birds and cats, you can explain what's going on simply in terms of cause and effect. Now, human language is more complex, but if you happen to have determinist beliefs, at some level you believe it's all cause and effect, right? So, when describing why and how people use words, would an ideal observer need to talk about the meanings of words at all, or would the concept of meaning drop out as unnecessary?

Since no one else has answered your question, I'll chime in. I confess that I find it hard to see how any explanation of human communication purely at the level of (say) sounds and scribbles, with no reference to the meaning conveyed by sounds and scribbles, could avoid leaving out something important. But I'm no expert on this topic, so all I can do is recommend reading the SEP entry on "Eliminative Materialism," found here. I'm going to read it now myself.

A common defense of an unethical act is to say, "If I didn't do it, someone else would." Let's say for the sake of argument that such a claim is true. Is it a credible defense? I wonder if a utilitarian in particular should be receptive to this line of thought.

Good question. Yes, utilitarianism is a form of consequentialism and, as the term suggests, the concern is with the net consequences of action. If some consequence is inevitable (imagine this involves an injury) and it cannot be prevented, then it may be an open question about who brings about the consequence. I note that this would be an "open question," because a utilitarian might still have good reasons to be very concerned about who does the act. Let's say you and I have applied for a job that will result in one of us (unfairly) injuring someone and, for some reason, this unfair injury cannot be prevented. I get the job and reason that, well, if I don't do it, you would. It still may be worse for me to do the act for, having done it, perhaps I have a weak character and am more likely to do far more unjust acts (than you). But, setting aside this additional way of measuring and comparing consequences, it is usually the non-utilitarian (the Kantian or advocate of virtue theory) who claim that it matters a great deal who actually does the harm. For some, it is a matter of integrity. For a classic case for integrity do a search for Bernard Williams on integrity against utilitarianism.

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